Preprint of the project: SFB 701: Spectral Structures and Topological Methods in Mathematics - Project B3

Numerical Analysis of equivariant evolution equations

14-010 Thorsten Hüls, Christian Pötzsche.
Qualitative analysis of a nonautonomous Beverton-Holt Ricker model

We explore a planar discrete-time model from population dynamics subject to a general aperiodic time-varying environment in order to illustrate the recent theory of nonautonomous dynamical systems. Given such a setting, the mathematical standard tools from classical dynamical systems and bifurcation theory cannot be employed, since for instance equilibria typically do not exist or eigenvalues yield no stability information. For this reason, we apply a combination of recent analytical and numerical techniques adequate to tackle such situations.